Shamil Asgarli

Starting Fall 2022, I am an assistant professor in the Department of Mathematics and Computer Science at Santa Clara University. Previously, I was a postdoctoral fellow at the University of British Columbia with Dragos Ghioca and Zinovy Reichstein as my mentors.

I received my PhD from Brown University (May 2019) under the supervision of Brendan Hassett.

I am interested in algebraic geometry and arithmetic geometry, with recent foray into algebraic graph theory. Much of my work has focused on geometry and combinatorics over finite fields, but I am also interested in problems in characteristic 0.

Email: sasgarli@scu.edu

Papers and preprints

1. A New Proof of Warning's Second Theorem The American Mathematical Monthly Vol. 125, No. 6 (2018), 549--553.
2. The Picard group of the moduli of smooth complete intersections of two quadrics (with Giovanni Inchiostro), Trans. Amer. Math. Soc., Vol. 372, No. 5 (2019) p. 3319--3346.
3. Sharp Bertini theorem for plane curves over finite fields, Canadian Math. Bulletin. Vol. 62 (2), 2019 p. 223--230.
4. Transverse lines to surfaces over finite fields (with Lian Duan and Kuan-Wen Lai), manuscripta mathematica (165) pages 135--157 (2021) Erratum
5. On the proportion of transverse-free plane curves (with Brian Freidin), Finite Fields and Their Applications. Vol 72, June 2021
6. A Bertini type theorem for pencils over finite fields (with Dragos Ghioca), Finite Fields and Their Applications. Vol 77, Jan 2022
7. Bijective Cremona transformations of the plane (with Kuan-Wen Lai, Masahiro Nakahara, Susanna Zimmermann), Selecta Mathematica, New Series 28, 53 (2022)
8. Van Lint-MacWilliams' conjecture and maximum cliques in Cayley graphs over finite fields (with Chi Hoi Yip), Journal of Combinatorial Theory, Series A, Vol. 192 (2022), 105667.
9. The EKR-module property of pseudo-Paley graphs of square order (with Sergey Goryainov, Huiqiu Lin, and Chi Hoi Yip), Electron. J. Combin. 29 (2022), no. 4, Paper No. P4.33, 19 pp.
10. Smoothness in pencils of hypersurfaces over finite fields (with Dragos Ghioca), Bulletin of the Australian Mathematical Society
(2023), Volume 107, Issue 1, February 2023, 85-94.
11. Linear families of smooth hypersurfaces over finitely generated fields (with Dragos Ghioca and Zinovy Reichstein), Finite Fields and Their Applications, Volume 87, March 2023, 102169.
12. Plane curves giving rise to blocking sets over finite fields (with Dragos Ghioca and Chi Hoi Yip), Des. Codes Cryptogr. 91 (2023), no. 11, 3643–3669.
13. Existence of pencils with nonblocking hypersurfaces (with Dragos Ghioca and Chi Hoi Yip), Finite Fields and Their Applications, Vol 92, December 2023, 102283.
14. Transverse linear subspaces to hypersurfaces over finite fields (with Lian Duan and Kuan-Wen Lai), Finite Fields and Their Applications, Vol. 95, March 2024, 102396.
15. Tangent-filling plane curves over finite fields (with Dragos Ghioca), Bulletin of the Australian Mathematical Society, Vol. 109, Issue 2, April 2024, pp. 301--315.
16. A Fair Shake: How close can the sum of n-sided dice be to a uniform distribution? (with Michael Hartglass, Daniel Ostrov and Byron Walden), American Mathematical Monthly, Vol. 131, Issue 7 (2024), 608--617.
17. Most plane curves over finite fields are not blocking (with Dragos Ghioca and Chi Hoi Yip), Journal of Combinatorial Theory, Series A, Vol. 204, May 2024, 105871.
18. The subspace structure of maximum cliques in pseudo-Paley graphs from unions of cyclotomic classes (with Chi Hoi Yip), Finite Fields and Their Applications, Vol. 99, October 2024, 102492.
19. Linear system of hypersurfaces passing through a Galois orbit (with Dragos Ghioca and Zinovy Reichstein), Research in Number Theory, Volume 10, article number 84, (2024).
20. Frobenius nonclassical hypersurfaces (with Lian Duan and Kuan-Wen Lai), Mathematische Zeitschrift, Volume 309, article number 18, (2025).
21. Plane-filling curves of small degree over finite fields (with Dragos Ghioca), to appear in Rocky Mountain Journal of Mathematics.
22. Linear system of geometrically irreducible plane cubics over finite fields (with Dragos Ghioca), Bulletin of the Australian Mathematical Society, published online (27 February 2025)
23. Chromatic quasisymmetric functions of the path graph (with Farid Aliniaeifard, Maria Esipova, Ethan Shelburne, Stephanie van Willigenburg, and Tamsen Whitehead McGinley), Annals of Combinatorics (May 2025).
24. Counting subgraphs of coloring graphs (with Sara Krehbiel, Howard Levinson, and Heather Russell), Graphs and Combinatorics, Volume 41, article number 82, (2025).
25. Proportion of blocking curves in a pencil (with Dragos Ghioca and Chi Hoi Yip), Discrete Mathematics 349 (2026), no. 1, Paper No. 114668, 7pp.
26. Mutual position of two smooth quadrics over finite fields (with Chi Hoi Yip), Designs, Codes and Cryptography, published online (6 July 2025).
27. Hypersurfaces passing through the Galois orbit of a point (with Jonathan Love and Chi Hoi Yip).
28. Coloring graphs as complete graph invariants (with Sara Krehbiel and Howard Levinson).
29. Collision of orbits for families of polynomials defined over fields of positive characteristic (with Dragos Ghioca).

Expository notes and other documents

Teaching at Santa Clara University

Teaching at UBC (past)

Here are some of the classes I taught at the University of British Columbia (as a postdoctoral fellow):

Teaching at Brown (past)

Here are some of the classes I TA-ed or taught at Brown (as a graduate student):

I completed the Certificate I: Reflective Teaching Program through the Sheridan Center for Teaching and Learning.